A common-mode inductance impedance measurement method based on a vector network analyzer

Abstract

The application discloses a common-mode inductance impedance measurement method based on a vector network analyzer, and comprises the following steps: firstly, a measurement clamp is constructed; through preliminary calibration of the distributed parameters of the measurement clamp, initial values of clamp inductance L2 and clamp capacitance C2 in the measurement clamp are obtained; then, the admittance of the measurement clamp and the common-mode inductor is measured by using the vector network analyzer, and the impedance curve of the common-mode inductor is calculated; finally, the initial values of the clamp inductance L2 and the clamp capacitance C2 are corrected based on the impedance analyzer; for the measurement clamps in the same batch, the impedance curve of the common-mode inductor is calculated by using the corrected clamp inductance L2 and clamp capacitance C2 values without further calibration or correction.

Description

Technical Field

[0001] This invention belongs to the field of electronic component measurement technology, and more specifically, relates to a common-mode inductance impedance measurement method based on a vector network analyzer. Background Technology

[0002] Common-mode inductor impedance measurement is fundamental to the design of common-mode inductor filters (F. Fan, KYSee, X. Liu, et al., Systematic Common-Mode Filter Design for Inverter-Driven Motor System Based on in-Circuit Impedance Extraction, IEEE Transactions on Electromagnetic Compatibility[J], 2020, 62(5): 1711-1722.). Common-mode inductor impedance measurement is primarily performed using an impedance analyzer. However, impedance analyzers are expensive, making large-scale industrial online detection and measurement difficult.

[0003] To address the aforementioned issues, a common-mode inductance and impedance measurement method based on a vector network analyzer was proposed. However, due to the influence of cable contact capacitance (J. Yao, S. Wang and H. Zhao, Measurement Techniques of Common Mode Currents, Voltages, and Impedances in a Flyback Converter for Radiated Emi Diagnosis, IEEE Transactions on Electromagnetic Compatibility[J], 2019, 61(6): 1997-2005.) and fixture distributed capacitance and inductance (HMJie, SPGao, ZYZhao, et al., VNA-Based Fixture Adapters for Wideband Accurate Impedance Extraction of Single-Phase Emi Filtering Chokes, IEEE Transactions on Industrial Electronics[J], 2023, 70(8): 7821-7831.), this method exhibits significant errors at high frequencies. J. Yao proposed a cable parasitic parameter compensation method to eliminate cable parasitic effects. HMJie eliminates parasitic effects from fixtures through a specialized fixture design method and a de-embedding process. However, this method relies on specialized fixtures with complex structures, making large-scale industrial applications difficult. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a common-mode inductance impedance measurement method based on a vector network analyzer. By calibrating the fixture distribution parameters through an algorithm, high-precision measurement of common-mode inductance up to 120MHz can be achieved.

[0005] To achieve the above-mentioned objective, this invention provides a common-mode inductor impedance measurement method based on a vector network analyzer. This method is used for measuring the impedance of an inductor model composed of a common-mode inductor, a fixture, and a vector network analyzer. The common-mode inductor is soldered onto the fixture, with the soldering endpoints denoted as c and d. The fixture is connected to ports 1 and 2 of the vector network analyzer, with the connection endpoints denoted as a and b. The method comprises the following steps:

[0006] (1) Construct a measuring fixture;

[0007] (2) By performing preliminary calibration of the distributed parameters of the measuring fixture, the initial values ​​of the fixture inductance L2 and fixture capacitance C2 in the measuring fixture are obtained;

[0008] (3) Measure the admittance of the fixture and common-mode inductor using a vector network analyzer;

[0009] (4) Calculate the impedance curve of the common mode inductor based on the admittance of the fixture and the common mode inductor, as well as the fixture inductance L2 and fixture capacitance C2;

[0010] (5) Based on the impedance analyzer, correct the initial values ​​of the clamp inductance L2 and clamp capacitance C2;

[0011] (6) The impedance curve of the common mode inductor is calculated using the corrected values ​​of fixture inductance L2 and fixture capacitance C2 for all measuring fixtures in the same batch.

[0012] The objective of this invention is achieved as follows:

[0013] This invention relates to a common-mode inductor impedance measurement method based on a vector network analyzer. First, a measurement fixture is constructed. Through preliminary calibration of the distributed parameters of the measurement fixture, initial values ​​of the fixture inductance L2 and fixture capacitance C2 are obtained. Then, the admittance of the fixture and the common-mode inductor is measured using a vector network analyzer, thereby calculating the impedance curve of the common-mode inductor. Next, the initial values ​​of the fixture inductance L2 and fixture capacitance C2 are corrected using an impedance analyzer. For measurement fixtures in the same batch, no further calibration or correction is required; the corrected values ​​of the fixture inductance L2 and fixture capacitance C2 are used to calculate the impedance curve of the common-mode inductor.

[0014] Meanwhile, the common-mode inductance impedance measurement method based on a vector network analyzer of the present invention also has the following beneficial effects:

[0015] (1) This invention proposes a method for measuring the impedance of a common-mode inductor using a vector network analyzer and its fixture, which realizes precise measurement of the impedance of a common-mode inductor using a vector network analyzer with a frequency up to 120MHz.

[0016] (2) Compared with the method of eliminating the interference of fixture parasitic effect in the de-embedding process, the present invention has a simple algorithm and high accuracy.

[0017] (3) The measuring fixture designed in this invention does not require recalibration or correction of parameters after the fixture distribution parameters are calibrated, and is still applicable to the measurement of common mode inductors with other inductance values.

[0018] (4) Compared with the traditional 120MHz impedance analyzer, the present invention has low hardware cost and is easy to be applied in large-scale industrial applications. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the common-mode inductance impedance measurement method based on a vector network analyzer according to the present invention.

[0020] Figure 2This is a flowchart for calibrating the distributed parameters of the measuring fixture;

[0021] Figure 3 This is a comparison curve of the common-mode inductor impedance measured by a vector network analyzer and an impedance analyzer;

[0022] Figure 4 This is an example of measuring impedance curves using a vector network analyzer and an impedance analyzer. Detailed Implementation

[0023] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0024] Example

[0025] Figure 1 This is a schematic diagram of the common-mode inductance impedance measurement method based on a vector network analyzer, as described in this invention.

[0026] In this embodiment, the present invention provides a common-mode inductor impedance measurement method based on a vector network analyzer, used for an inductor impedance measurement model composed of a common-mode inductor, a fixture, and a vector network analyzer, such as... Figure 1 As shown, the common mode inductor is soldered onto the fixture, and the soldering endpoints are denoted as c and d; the fixture is connected to port1 and port2 terminals of the vector network analyzer, and the connection endpoints are denoted as a and b;

[0027] exist Figure 1 In the diagram, box A represents the equivalent circuit model of the common-mode inductor, including the equivalent resistance R1, equivalent inductance L, and winding equivalent capacitance C1; box B represents the equivalent circuit of the clamp, including clamp capacitance C2 and clamp inductance L2; the clamp equivalent model proposed by J.Yao and HMJie is more complex, and is simplified to box B here. Box C represents the equivalent model of the vector network analyzer, including the AC signal source AC, measuring resistor Rm, and vector voltmeter.

[0028] Below, we will describe in detail the process of common-mode inductance impedance measurement, specifically including the following steps:

[0029] (1) Construct a measuring fixture;

[0030] The measuring fixture includes five component soldering positions: TL1, TC1, TC2, P1, and P2. Each soldering position has two endpoints. TL1 and TC1 are connected in parallel, forming branch Z. p Then, branch Zp is connected in series with TC2 to form branch Z. s Finally, P1 and P2 are connected in series in the Z branch.s The two ends.

[0031] (2) Initial values ​​of clamp inductance L2 and clamp capacitance C2 are obtained by preliminary calibration of clamp distribution parameters;

[0032] In this embodiment, as Figure 2 As shown in the first figure, the fixture includes two SMA interfaces, an inductor position TL1, a parallel capacitor position TC1, and a series capacitor position TC2. TL1 and TC1 are connected in parallel, and the parallel circuit is then connected in series with TC2. The two ends of the circuit are connected in series with the SMA ports and then connected to the vector network analyzer instrument.

[0033] Take the nominal inductor L3, nominal capacitor C3, and C L During calibration, the nominal inductor L3 is surface-mounted at fixture TL1, the nominal capacitor C3 is surface-mounted at TC1, and the nominal capacitor C is surface-mounted at TC2. L Considering the circuit diagram under distributed parameters, as shown below. Figure 2 As shown in the second figure. L3 and L2 are connected in series to form a series branch ②, and the equivalent inductance of the series branch ② is denoted as L4; the series branch ② is connected in parallel with C2 and C3 respectively to form a parallel branch ②; the equivalent capacitance of C2 and C3 in parallel is C4; the parallel branch ② and C L They are connected in series to construct an equivalent circuit for fixture calibration and then connected to a vector network analyzer.

[0034] Will Figure 2 The second image in the middle is simplified to obtain Figure 2 The equivalent circuit shown in the third figure has L4 and C4 connected in parallel as parallel branch ③, which is then connected to C... L The circuit is connected in series, where L4 = L2 + L3; C4 = C2 + C3; finally, the above circuit is connected to a vector network analyzer.

[0035] The inductance L4, which is common to both the fixture and the nominal inductance, is measured using the method described in ZL202011292243.9 and IEEE Transactions on Instrumentation and Measurement, 2022, 71. The capacitance C4, which is common to both the nominal capacitance and the distributed capacitance, is also measured. Thus, the fixture inductance can be calculated as L2 = L4 - L3, and the fixture capacitance as C2 = C4 - C3.

[0036] (3) Measure the admittance of the fixture and common-mode inductor using a vector network analyzer;

[0037] Based on the aforementioned measuring fixture, a common-mode inductor is soldered to TL1, TC1 is left floating, and TC2 is directly short-circuited. SMA ports are soldered to P1 and P2 and connected to a vector network analyzer.

[0038] like Figure 2In the fixture model shown in the first figure, TC1 is suspended, TC2 is directly connected, a common mode inductor is inserted at TL1, and then connected to a vector network analyzer.

[0039] Set the vector network analyzer's frequency range to 0-120MHz and the measurement mode to S21 Smith; then, take values ​​within the frequency range and measure different frequencies f. i The corresponding admittance data is denoted as A. i And the imaginary part of the admittance is B i , i = 1, 2, ..., n, where n represents the number of frequency sampling points.

[0040] (4) Calculate the impedance curve of the common mode inductor based on the admittance of the fixture and the common mode inductor, as well as the fixture inductance L2 and fixture capacitance C2;

[0041] make Figure 1 If the complex impedance between points c and d is Z1(ω), then the complex impedance between points a and b is:

[0042]

[0043] According to CN202011292243.9, the complex admittance between points a and b obtained from the Smith chart of the vector network analyzer is...

[0044]

[0045] Based on the admittance data obtained from step (2): f i The frequency point of the sweep frequency has an angular frequency ω. i =2πf i A i B is the real part of the admittance G(ω). i Let G(ω) be the imaginary part of the admittance. Then the complex admittance G(ω) at each frequency can be expressed as:

[0046] G(ω i ) = A i +jB i (3)

[0047] (3) Inductor impedance measurement algorithm based on vector network analyzer

[0048] From equations (2) and (3), we can obtain:

[0049]

[0050] Then the complex impedance between points a and b can be obtained as:

[0051]

[0052] Equation (5) represents the measured impedance between points a and b, and Equation (1) is the analytical expression for the impedance between points a and b. Combining these two equations, they are equal, i.e.

[0053]

[0054] In equation (6), ω i =2πf i get:

[0055]

[0056] In equation (7), the right side represents the measured value, and the left side represents the analytical expression for the impedance between points a and b. The impedance of the common-mode inductor is Z1(2πf i ) is the quantity to be solved, and j2πfL2 and j2πfC2 are the inductance and capacitance represented by the distributed parameters of the clamp and the wire, respectively.

[0057] The inductor impedance Z1(2πfL2) can be inverted using equation (7) by measuring the distributed inductance j2πfL2 and the distributed capacitance j2πfC2. i ).make:

[0058] Z3(2πf i )=Z1(2πf i )+j2πf i L2 (8)

[0059] Equation (7) can be simplified as follows:

[0060]

[0061] in,

[0062] Solving equation (9) yields:

[0063]

[0064] The complex impedance of the inductor is obtained from equation (8):

[0065]

[0066] Impedance Z Inductance Let the modulus of its complex impedance be the square root of the sum of the squares of the real and imaginary parts of the impedance. The mathematical operator `abs()` is used to calculate the modulus. Therefore, the measured impedance is:

[0067] y i =abs(Z1(2πf i (12)

[0068] (5) Correct the initial values ​​of the clamp inductance L2 and clamp capacitance C2, and obtain the corrected impedance curve of the model inductor.

[0069] (5.1) Generate L2 and C2 meshes;

[0070] Based on the initial values ​​of clamp inductor L2 and clamp capacitor C2, multiple points are taken on both sides of L2 and C2 with a fixed step, resulting in a grid of inductance and capacitance values.

[0071] (5.2) Substitute the inductance and capacitance values ​​corresponding to each grid point in grids L2 and C2 into the common-mode inductor impedance curve to obtain the common-mode inductor impedance curve corresponding to each grid point. Let y be the common-mode inductor impedance curve corresponding to the j-th grid point. i_j y i_j The corresponding inductance and capacitance values ​​are L 2j C 2j ;

[0072] (5.3) With the same fixture and common-mode inductor, the impedance curve measured by the impedance analyzer is Y. i The common-mode inductor impedance curves calculated for each grid point are y i_j Calculate the root mean square error of the two curves at each grid point;

[0073]

[0074] (5.4) Select the minimum root mean square error, denoted as RMSE. min If the root mean square error (RMSE) min Less than the set value RMSE set RMSE min <RMSE set Then save RMSE. min The corresponding L 2j C 2j y i_j Then proceed to step (5.5); otherwise, reduce the step size of the values ​​on both sides of L2 and C2 to further refine the grid spacing, and then return to step (5.1) for the next iteration; if RMSE is still not satisfied after k consecutive iterations... min <RMSE set Then compare the minimum root mean square error (RMSE) after the k-th iteration. min_k The minimum root mean square error (RMSE) after the (k-1)th iteration min_k-1 Is the difference less than the threshold RMSE? Δ If the condition is met, the iteration ends, and the RMSE is saved. min_k The corresponding L 2j C 2j y i_j Otherwise, further refine the grid spacing and return to step (5.1);

[0075] (5.5) Output the corrected values ​​of the fixture inductance L2 and fixture capacitance C2, L2 = L 2j C2 = C 2j .

[0076] Finally, for fixtures in the same batch, no further calibration or correction is required; the impedance curve of the common-mode inductor is calculated using the corrected values ​​of fixture inductance L2 and fixture capacitance C2.

[0077] Instance verification

[0078] 1. Example of measuring the impedance of a nominal 28.5uH common-mode inductor;

[0079] The equipment used includes a PCB fixture, a common-mode inductor, a vector network analyzer, and a PC. The fixture is connected to the vector network analyzer (specifically, a CopperMountain TR1300 / 1 model) via a coaxial cable. First, the distributed inductance and capacitance of the fixture are calibrated. Then, the vector network analyzer measures the common-mode inductor admittance. Finally, the admittance data is imported into an impedance curve to calculate the common-mode inductor impedance.

[0080] The specific implementation steps are as follows:

[0081] (1) Preliminary calibration of fixture distribution parameters.

[0082] Figure 2 A nominal 4.7uH inductor is surface-mounted at TL1, a nominal 10pF capacitor is surface-mounted at TC1, and a nominal 47pF capacitor is surface-mounted at TC2. The inductance L4, shared by the fixture and the nominal inductor, and the capacitance C4, shared by the nominal and distributed capacitances, are measured using the methods described in ZL202011292243.9 and IEEE Transactions on Instrumentation and Measurement, 2022, 71. The measurement results are: L4 = 5.01uH, C4 = 11.49pF.

[0083] The distributed inductance of the fixture is L2 = L4 - L3 = 5.01uH - 4.7uH = 0.31uH, and the distributed capacitance is C2 = C4 - C3 = 11.49pF - 10pF = 1.49pF.

[0084] (2) Measure the common-mode inductance and the admittance of the fixture.

[0085] In the fixture model, TC1 is left floating, TC2 is directly connected, a common-mode inductor is inserted at TL1, and then a vector network analyzer is connected. The frequency range of the vector network analyzer is set to 0-120MHz, and the measurement mode is set to S21 Smith. The array of admittance data acquired by the vector network analyzer consists of three columns, each representing the frequency f. i Admittance Real Part A i And the imaginary part of admittance B i Then, the impedance of the common-mode inductor at each frequency point is calculated from the data impedance curve at each frequency point, such as... Figure 3 As shown by the solid line in the middle.

[0086] (3) Precise calibration of distributed parameters based on impedance analyzer measurement data.

[0087] Due to the error between the nominal and actual values ​​of inductors and capacitors, and the differences between the distributed parameters of vector network analyzers and impedance analyzers. Figure 3 The common-mode inductance measured by both instruments has a large error at high frequencies. Next, the impedance analyzer will be used to calibrate the vector network analyzer.

[0088] ① Fitting the measured impedance curve using an impedance analyzer

[0089] For the same set of common-mode inductors, the impedance curve measured by the impedance analyzer is [XX]. t YY t ], of which XX t For frequency, YY t For impedance, such as Figure 3 As shown by the dashed line. Since two instruments are used for measurement, the operators may have used different frequency spacing standards. For example, in this experiment, the impedance analyzer's frequency data XX... t Using logarithmic coordinates with equal intervals, the frequency data X of the vector network analyzer t The instruments were arranged at equal intervals. However, the frequency coordinates of the two instruments were inconsistent, making calculations impossible.

[0090] Therefore, it is necessary to fit the measured impedance curve of the impedance analyzer and interpolate it to the frequency coordinate f of the vector network analyzer. i The corresponding impedance. Here, a 9th-order polynomial is used to fit the impedance curve measured by the impedance analyzer. The frequency coordinate f of the vector network analyzer is calculated by interpolation of the fitted curve. i The corresponding impedance Y i Therefore, the impedance curve measured by the impedance analyzer is [f i ,Y i ].

[0091] ② Generate L2 and C2 meshes;

[0092] Set the inductor array L2X:[Linitial -L range :L_ space :L initial +L range According to step (1), L2 is around 0.31uH. Set L... initial =0.31uH, L range =0.1uH, L_ space =0.1uH. Then L2X is the array [0.21:0.1:0.41]*uH.

[0093] Set the capacitor array: C2X:[C initial -C range :C_ space :C initial +C range According to step (1), L2 C2 is around 1.49 pF. Set C... initial =1.49pF, C range =1.49pF, C_ space =1pF. Then C2X is the array [0:1:2.98]*uH.

[0094] ③ Calculate the common-mode inductance impedance curves of the L2 and C2 grid points to obtain the common-mode inductance impedance curve y measured by the vector network analyzer. i =Z Inductance (f i ).

[0095] ④ Calculate the root mean square error (RMSE) of the impedance curves of the impedance analyzer and the vector network analyzer corresponding to grid points L2 and C2. By iterating through the RMSE corresponding to each grid point, the minimum RMSE is found at grid points L2 = 0.388 μH, C2 = 0.08 pF, and RMSE = 14.40. The final comparison between the impedance curves measured by the vector network analyzer and the impedance curves measured by the impedance analyzer is shown below. Figure 4 As shown.

[0096] Example of measuring the impedance of a nominal 350uH common-mode inductor;

[0097] The nominal 350uH common-mode inductor impedance was measured using the same fixture from the example of measuring the nominal 28.5uH common-mode inductor impedance. Since it was from the same batch of fixtures, the same fixture parameters were used: L2 = 0.388uH, C2 = 0.08pF. The calculated RMSE_min = 41.95.

[0098] The 350uH common-mode inductor and its fixture were calibrated using an impedance analyzer. The operation in the nominal 28.5uH common-mode inductor impedance measurement example was repeated. The calculation results are as follows: L2 = 0.45uH, C2 = 0.005pF, RMSE = 41.80.

[0099] The comparison reveals an error of 0.35%, which may be due to variations in fixtures from the same batch or inconsistencies in the experimental environment.

[0100] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A common-mode inductor impedance measurement method based on a vector network analyzer, used for an inductor impedance measurement model consisting of a common-mode inductor, a fixture, and a vector network analyzer, wherein, A common-mode inductor is soldered onto a fixture, with the soldering endpoints denoted as c and d; the fixture is connected to port 1 and port 2 terminals of a vector network analyzer, with the connection endpoints denoted as a and b; the feature is that it includes the following steps: (1) Construct a measuring fixture; The measuring fixture includes five component soldering positions: TL1, TC1, TC2, P1, and P2. Each soldering position has two endpoints. TL1 and TC1 are connected in parallel, forming branch Z. p Then, branch Z p Connected in series with TC2, forming branch Z s Finally, P1 and P2 are connected in series in branch Z. s The two ends; (2) By performing preliminary calibration of the distributed parameters of the measuring fixture, the initial values ​​of the fixture inductance L2 and fixture capacitance C2 in the measuring fixture are obtained; (2.1) Take the nominal inductance L3, nominal capacitance C3, and C2. L The circuit that connects to the measuring fixture; The nominal inductor L3 is surface-mounted at TL1 of the measuring fixture, the nominal capacitor C3 is surface-mounted at TC1, and the nominal capacitor C is surface-mounted at TC2. L SMA ports are welded to P1 and P2 and connected to a vector network analyzer; (2.2) Equivalent circuit for obtaining the initial values ​​of the measuring fixture inductance L2 and the fixture capacitance C2; Connect the nominal inductor L3 and the clamp inductor L2 in series, and denote this series branch as Z. s1 Then connect the clamp capacitor C2 and the nominal capacitor C3 in parallel in the series branch Z. s1 Let Z be the total number of parallel branches at both ends. p Finally, the nominal capacitor C L Series Z p On the branch, an equivalent circuit for fixture calibration is constructed; (2.3) Simplify the equivalent circuit; Let L4 be the equivalent inductance of the nominal inductance L3 and the clamp inductance L2 connected in series, and let C4 be the equivalent capacitance of the clamp capacitance C2 and the nominal capacitance C3 connected in parallel. Then the model established in step (2.2) is simplified to: the equivalent inductance L4 and the equivalent capacitance C4 are connected in parallel to form the parallel branch Z. p parallel branch Z p Then compare with the nominal capacitor C L Series; In the simplified equivalent circuit, the nominal inductance L4 is not connected to the nominal capacitance C. L The connected end is terminal a, denoted by the nominal capacitance C. L The end not connected to the equivalent capacitance C4 is the access endpoint b, which is then connected to the vector network analyzer; (2.4) Obtain the initial values ​​of the fixture inductance L2 and fixture capacitance C2; Measure the equivalent inductance L4 and equivalent capacitance C4, then calculate the fixture inductance as L2 = L4 - L3; and the fixture capacitance as C2 = C4 - C3. (3) Measure the admittance of the fixture and common-mode inductor using a vector network analyzer; (3.1) Weld a common mode inductor to TL1 in the measuring fixture, leave TC1 floating, and directly short-circuit TC2. Weld SMA ports to P1 and P2 and connect them to the vector network analyzer. (3.2) Set the frequency range of the vector network analyzer to 0-120MHz and the measurement mode to S21 Smith; then take values ​​within the frequency range and measure different frequencies f. i The corresponding admittance data is denoted as A. i And the imaginary part of the admittance is B i , , Indicates the number of frequency sampling points; (4) Calculate the impedance curve of the common-mode inductor based on the admittance of the fixture and the common-mode inductor, as well as the fixture inductance L2 and fixture capacitance C2: ； in, Indicates the first Impedance curves of common-mode inductors calculated at each frequency point The vector network analyzer measures the first... One frequency point, Represents frequency The real and imaginary parts of the measured admittance data; To express modulo, The complex impedance of the common-mode inductor, Let a be the complex impedance between points a and b. For measuring resistance in a vector network analyzer; (5) Based on the impedance analyzer, correct the initial values ​​of the fixture inductance L2 and fixture capacitance C2; (5.1) Generate L2 and C2 meshes; Based on the initial values ​​of clamp inductor L2 and clamp capacitor C2, multiple points are taken on both sides of L2 and C2 with a fixed step, resulting in a grid of inductance and capacitance values. (5.2) Substitute the set of inductance and capacitance values ​​corresponding to each grid point in L2 and C2 into the common-mode inductor impedance curve to obtain the common-mode inductor impedance curve corresponding to each grid point. Let the first grid point be denoted as _____. The common-mode inductor impedance curves corresponding to each grid point are as follows: , The corresponding inductance and capacitance values ​​are L 2j C 2j ; (5.3) The impedance curves of the same fixture and common-mode inductor measured using an impedance analyzer are as follows: The common-mode inductor impedance curves calculated for each grid point are as follows: Calculate the root mean square error of the two curves at each grid point; ； (5.4) Select the minimum root mean square error, denoted as . If the root mean square error Less than the set value ,Right now Save The corresponding L 2j C 2j , Then proceed to step (5.5); otherwise, reduce the step size of the values ​​on both sides of L2 and C2 to further refine the grid spacing, and then return to step (5.1) for the next iteration; if the condition is still not met after k consecutive iterations... Then compare the minimum root mean square error after the k-th iteration. Minimum root mean square error after the (k-1)th iteration Is the difference less than the threshold? If the condition is met, the iteration ends and the data is saved. The corresponding L 2j C 2j , Otherwise, further refine the grid spacing and return to step (5.1); (5.5) Output the corrected values ​​of the fixture inductance L2 and fixture capacitance C2, L2 = L 2j C2=C 2j ; (6) The impedance curve of the common mode inductor is calculated using the corrected values ​​of fixture inductance L2 and fixture capacitance C2 for all measuring fixtures in the same batch.

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